🚀 DSA + Patterns + Algorithms 🚀

One of my post about 6 months DSA Plan is something most of the people liked

https://www.linkedin.com/posts/anandwana001_leetcode-androiddev-coding-activity-7211571579388895232-eHHO?utm_source=share&utm_medium=member_desktop

So, I thought to write this detailed article.

In this article today, we are going to each topic in detail and see what all things we need to prepare as per our target of 6-Months DSA Journey

Index:

1. From the post
2. Detailed 6 months roadmap
3. All Patterns & Technique to Solve a question
4. List of all Algorithms with Time & Space Complexity

From the Post

Month 1: Basics and Arrays

Week 1: Introduction and Basics

📚 Importance of DSA

⏳ Time/Space Complexity

🧮 Big O, Theta, Omega

🔍 Linear and Binary Search

Week 2: Arrays

📋 Array basics

⚙️ Operations (insert, delete, traverse)

🗄️ 1D/2D arrays

📝 Practice

Week 3: Arrays (continued)

↔️ Two-pointer technique

🔄 Sliding window

📝 Practice

Week 4: Strings

🔤 String basics

🔧 Operations and functions

🔍 Pattern searching (Naive, KMP, Rabin-Karp)

📝 Practice

Month 2: Linked Lists and Stacks

Week 5: Linked Lists

🔗 Basics and types (Singly, Doubly, Circular)

⚙️ Operations

📝 Practice

Week 6: Advanced Linked Lists

🚀 Advanced problems

📝 Practice

Week 7: Stacks

🥞 Stack basics

⚙️ Operations (push, pop, peek)

🛠️ Implementation

📊 Applications

📝 Practice

Week 8: Queues

🚶 Queue basics

⚙️ Operations (enqueue, dequeue)

🛠️ Implementation

🧩 Types (simple, circular, priority)

📝 Practice

Month 3: Trees

Week 9: Trees

🌳 Basics and types

🔄 Traversals (in-order, pre-order, post-order)

Week 10: Binary Search Trees (BST)

🔍 BST properties

⚙️ Operations

📝 Practice

Week 11: Balanced Trees

⚖️ AVL Trees

🔴⚫ Red-Black Trees

📝 Practice

Week 12: Heaps

⛰️ Heap basics

🔄 Types (min, max)

⚙️ Operations

🧮 Priority Queue

📝 Practice

Month 4: Graphs

Week 13: Graphs

🌐 Basics and types

🛠️ Representation

Week 14: Graph Traversal

🚶♂️ BFS

🌳 DFS

📝 Practice

Week 15: Shortest Paths

🛣️ Dijkstra's

🚀 Bellman-Ford

🌐 Floyd-Warshall

📝 Practice

Week 16: Minimum Spanning Tree (MST)

🌲 Kruskal's

🪵 Prim's

📝 Practice

Month 5: Advanced Topics

Week 17: Dynamic Programming (DP)

🤖 Basics

🧠 Memoization vs Tabulation

📜 Classic problems

Week 18: Advanced DP

🧩 Complex problems

📝 Practice

Week 19: Backtracking

🔙 Basics

🧩 Classic problems

📝 Practice

Week 20: Greedy Algorithms

💡 Basics

📜 Classic problems

📝 Practice

Month 6: Review and Mock Interviews

Week 21-24: Review and Practice

🔄 Arrays, Strings, Linked Lists, Stacks, Queues, Trees, Heaps, Graphs, DP, Backtracking, Greedy

📝 Mixed problems

Week 25: Mock Interviews

🎤 Participate in mock interviews

📝 Solve problems on LeetCode, HackerRank, CodeChef

Week 26: Final Revision

🔍 Focus on weak areas

📝 Final practice

Detailed Plan

Month 1: Foundations 🏗️

1. Week 1: Introduction to DSA 📚

- Topics: Basics of Data Structures and Algorithms, Time and Space Complexity

- Tasks:

- Read introductory materials on DSA.

- Understand Big O notation, best, average, and worst-case complexities.

- Practice basic complexity calculations.

2. Week 2: Arrays and Strings 🧵

- Topics: Arrays, Strings, Basic Operations, Sliding Window, Two Pointers

- Tasks:

- Study array operations: insertion, deletion, traversal, searching.

- Understand string manipulation techniques.

- Learn the sliding window technique and solve related problems.

- Practice two-pointer technique for array and string problems.

- Solve problems on platforms like LeetCode, HackerRank (easy level).

3. Week 3: Linked Lists 🔗

- Topics: Singly Linked List, Doubly Linked List, Circular Linked List

- Tasks:

- Implement basic linked list operations.

- Solve problems involving insertion, deletion, reversal of linked lists.

- Practice medium-level problems on linked lists.

4. Week 4: Stacks and Queues 📦

- Topics: Stack, Queue, Deque, Priority Queue

- Tasks:

- Understand stack and queue operations.

- Implement stack and queue using arrays and linked lists.

- Solve problems on stack and queue applications.

Month 2: Trees and Graphs 🌳

1. Week 1: Trees 🌲

- Topics: Binary Tree, Binary Search Tree

- Tasks:

- Learn tree traversal methods (in-order, pre-order, post-order).

- Solve problems on tree creation, traversal, and basic operations.

- Understand the properties of BST and solve related problems.

2. Week 2: Advanced Trees 🌴

- Topics: AVL Tree, Red-Black Tree, Segment Tree, Trie

- Tasks:

- Study self-balancing trees and their rotations.

- Solve problems on insertion, deletion in AVL and Red-Black trees.

- Implement and solve problems using Segment Trees and Tries.

3. Week 3: Graphs Basics 🗺️

- Topics: Graph Representation, DFS, BFS

- Tasks:

- Learn graph representations (adjacency matrix, list).

- Implement Depth First Search (DFS) and Breadth First Search (BFS).

- Solve basic graph traversal problems.

4. Week 4: Advanced Graphs 🧩

- Topics: Dijkstra’s Algorithm, Floyd-Warshall, Topological Sort

- Tasks:

- Understand shortest path algorithms.

- Solve problems on Dijkstra's and Floyd-Warshall algorithms.

- Practice problems involving topological sorting and cycle detection.

Month 3: Recursion and Backtracking 🔄

1. Week 1: Recursion Basics 🔁

- Topics: Basic Recursion, Mathematical Problems

- Tasks:

- Study the principles of recursion and base cases.

- Solve problems on factorial, Fibonacci, and basic mathematical problems.

2. Week 2: Recursion Applications 🔧

- Topics: Permutations, Combinations, Subset Sum

- Tasks:

- Solve problems involving permutations and combinations.

- Understand and implement subset sum problems using recursion.

3. Week 3: Backtracking 🔙

- Topics: N-Queens, Sudoku Solver, Maze Problems

- Tasks:

- Study the concept of backtracking and its applications.

- Solve classic backtracking problems like N-Queens, Sudoku, and maze-solving.

4. Week 4: Dynamic Programming Introduction 📈

- Topics: Basics of DP, Memoization vs Tabulation

- Tasks:

- Understand the difference between memoization and tabulation.

- Solve basic DP problems like Fibonacci, Coin Change (minimum coins).

Month 4: Advanced Dynamic Programming 🧮

1. Week 1: Intermediate DP Problems 🎯

- Topics: Knapsack, Longest Common Subsequence

- Tasks:

- Study and implement the 0/1 Knapsack problem.

- Solve problems on LCS, LIS (Longest Increasing Subsequence).

2. Week 2: Advanced DP Problems 🚀

- Topics: DP on Trees, DP with Bitmasks

- Tasks:

- Solve problems involving DP on tree structures.

- Understand and implement problems using bitmasking.

3. Week 3: DP Practice 🏋️

- Topics: Practice Mixed Problems

- Tasks:

- Solve a variety of DP problems from different categories.

- Focus on problems from competitive programming platforms.

4. Week 4: Review and Reinforce 🔍

- Topics: Review Key Concepts

- Tasks:

- Revise all major DP concepts and problems solved.

- Identify weak areas and reinforce them with additional practice.

Month 5: Sorting, Searching, and Miscellaneous 🔄

1. Week 1: Sorting Algorithms 🗃️

- Topics: Quick Sort, Merge Sort, Heap Sort

- Tasks:

- Understand and implement advanced sorting algorithms.

- Solve problems involving different sorting techniques.

2. Week 2: Searching Algorithms 🔍

- Topics: Binary Search, Search Variants

- Tasks:

- Study binary search and its applications.

- Solve problems on binary search and search variants (e.g., rotated array).

3. Week 3: Miscellaneous Algorithms 🎲

- Topics: Bit Manipulation, Greedy Algorithms

- Tasks:

- Learn and practice bit manipulation techniques.

- Understand the greedy approach and solve related problems.

4. Week 4: Mock Interviews and Problem Solving 🎤

- Tasks:

- Participate in mock interviews.

- Solve a variety of problems to simulate real interview conditions.

Month 6: Mock Interviews and Final Review 🏁

1. Week 1: System Design Basics 🏗️

- Topics: Basic Concepts of System Design

- Tasks:

- Study the fundamentals of system design.

- Understand key components like load balancing, caching, and databases.

2. Week 2: Mock Interviews 🎥

- Tasks:

- Participate in multiple mock interviews with peers or mentors.

- Focus on problem-solving speed and accuracy.

3. Week 3: Review and Reinforce 📘

- Topics: Review All Concepts

- Tasks:

- Revise key DSA concepts and problems.

- Solve problems in weaker areas identified during mocks.

4. Week 4: Final Preparation 🏆

- Tasks:

- Conduct final round of mock interviews.

- Relax and prepare mentally for actual interviews.

Patterns

Essential Coding Patterns for Interview Preparation

1. Two Pointers 🔄

- Applications: Array and string manipulation, such as finding pairs, triplets, or subarrays with a specific sum, and partitioning arrays.

- Examples: Reverse a string, remove duplicates from sorted array, container with most water.

2. Sliding Window 🪟

- Applications: Problems involving contiguous subarrays or substrings.

- Examples: Maximum sum subarray of size k, longest substring without repeating characters, minimum window substring.

3. Fast and Slow Pointers (Tortoise and Hare) 🐢🐇

- Applications: Cycle detection in linked lists, finding the middle of a linked list.

- Examples: Linked list cycle detection, finding the middle of a linked list, happy number.

4. Merge Intervals 🧩

- Applications: Problems involving overlapping intervals.

- Examples: Merge intervals, insert interval, meeting rooms.

5. Cyclic Sort 🔄

- Applications: Sorting problems where elements are in a known range.

- Examples: Find missing number, find all duplicates, find all missing numbers.

6. In-place Reversal of a Linked List 🔀

- Applications: Problems involving the reversal of linked list segments.

- Examples: Reverse a linked list, reverse every k-element sub-list, reverse a sub-list.

7. Tree Depth-First Search (DFS) 🌳

- Applications: Problems involving tree traversal, path finding, and subtree calculations.

- Examples: Binary tree path sum, all paths for a sum, sum of path numbers.

8. Tree Breadth-First Search (BFS) 🌲

- Applications: Level-order traversal of trees, shortest path in graphs.

- Examples: Binary tree level order traversal, zigzag traversal, connect level order siblings.

9. Binary Search 🔍

- Applications: Search problems in sorted arrays, search space reduction.

- Examples: Order-agnostic binary search, ceiling of a number, next letter.

10. Top K Elements 🏆

- Applications: Problems requiring finding the top k largest/smallest elements.

- Examples: Top k numbers, kth smallest number, k closest points to the origin.

11. K-way Merge 📚

- Applications: Merging sorted arrays, finding k closest elements.

- Examples: Merge k sorted lists, kth smallest number in M sorted lists, smallest range.

12. Topological Sort 🔄

- Applications: Ordering of tasks, finding cycles in directed graphs.

- Examples: Task scheduling, alien dictionary, minimum height trees.

13. Dynamic Programming (DP) 📈

- Applications: Optimization problems, problems with overlapping subproblems.

- Examples: 0/1 Knapsack, longest common subsequence, coin change problem.

14. Greedy Algorithms 💡

- Applications: Optimization problems where local optimal choices lead to global optimum.

- Examples: Interval scheduling maximization, fractional knapsack, minimum cost to connect ropes.

15. Bit Manipulation 🧮

- Applications: Problems involving bit operations, binary representation.

- Examples: Single number, complement of a number, count of set bits.

16. Backtracking 🔙

- Applications: Problems involving search through all possible solutions.

- Examples: N-Queens, sudoku solver, subsets.

17. Mathematical Problems ➕➗

- Applications: Problems requiring mathematical calculations, number theory.

- Examples: GCD, prime numbers, power of two.

Algorithms

Essential Algorithms with Time and Space Complexities

Sorting Algorithms 🗃️

1. Bubble Sort 🍾

- Time Complexity:

- Best: O(n)

- Average: O(n²)

- Worst: O(n²)

- Space Complexity: O(1)

2. Selection Sort 🔍

- Time Complexity:

- Best: O(n²)

- Average: O(n²)

- Worst: O(n²)

- Space Complexity: O(1)

3. Insertion Sort 📝

- Time Complexity:

- Best: O(n)

- Average: O(n²)

- Worst: O(n²)

- Space Complexity: O(1)

4. Merge Sort 🌊

- Time Complexity:

- Best: O(n log n)

- Average: O(n log n)

- Worst: O(n log n)

- Space Complexity: O(n)

5. Quick Sort ⚡

- Time Complexity:

- Best: O(n log n)

- Average: O(n log n)

- Worst: O(n²)

- Space Complexity: O(log n)

6. Heap Sort 🔼

- Time Complexity:

- Best: O(n log n)

- Average: O(n log n)

- Worst: O(n log n)

- Space Complexity: O(1)

Searching Algorithms 🔍

1. Linear Search 🚶

- Time Complexity:

- Best: O(1)

- Average: O(n)

- Worst: O(n)

- Space Complexity: O(1)

2. Binary Search 🚀

- Time Complexity:

- Best: O(1)

- Average: O(log n)

- Worst: O(log n)

- Space Complexity: O(1)

Graph Algorithms 🌐

1. Depth-First Search (DFS) 🌲

- Time Complexity: O(V + E)

- Space Complexity: O(V)

2. Breadth-First Search (BFS) 🏞️

- Time Complexity: O(V + E)

- Space Complexity: O(V)

3. Dijkstra’s Algorithm 🛤️

- Time Complexity: O(E + V log V) (using a priority queue)

- Space Complexity: O(V)

4. Floyd-Warshall Algorithm 🛡️

- Time Complexity: O(V³)

- Space Complexity: O(V²)

5. Kruskal’s Algorithm 🌉

- Time Complexity: O(E log E)

- Space Complexity: O(V)

6. Prim’s Algorithm ⛓️

- Time Complexity: O(E + V log V) (using a priority queue)

- Space Complexity: O(V)

Dynamic Programming 📈

1. Fibonacci Sequence 🌀

- Time Complexity:

- Recursive: O(2^n)

- Memoized: O(n)

- Iterative: O(n)

- Space Complexity:

- Recursive: O(n) (stack space)

- Memoized: O(n)

- Iterative: O(1)

2. 0/1 Knapsack 🎒

- Time Complexity: O(nW)

- Space Complexity: O(nW)

3. Longest Common Subsequence (LCS) 🧵

- Time Complexity: O(nm)

- Space Complexity: O(nm)

4. Coin Change 💰

- Time Complexity: O(nW)

- Space Complexity: O(W)

String Algorithms 🧶

1. Knuth-Morris-Pratt (KMP) Algorithm 🔍

- Time Complexity: O(n + m)

- Space Complexity: O(m)

2. Rabin-Karp Algorithm 📜

- Time Complexity:

- Best: O(n + m)

- Average: O(n + m)

- Worst: O(nm)

- Space Complexity: O(1)

3. Trie (Prefix Tree) 🌳

- Time Complexity:

- Insertion: O(m)

- Search: O(m)

- Deletion: O(m)

- Space Complexity: O(Alphabet Size m n)

Miscellaneous Algorithms 🎲

1. Quick Select 🎯

- Time Complexity:

- Best: O(n)

- Average: O(n)

- Worst: O(n²)

- Space Complexity: O(1)

2. Union-Find / Disjoint Set 🧩

- Time Complexity:

- Find: O(α(n))

- Union: O(α(n))

- Space Complexity: O(n)

3. Bit Manipulation 🧮

- Common Operations: O(1)

- Space Complexity: O(1)

Good luck with your preparation! 🍀

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https://topmate.io/anandwana001/1022452

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